On the perturbation and subproper splittings for the generalized inverse AT,S(2) of rectangular matrix A

In this paper, the perturbation and subproper splittings for the generalized inverse AT,S(2), the unique matrix X such that XAX=X, R(X)=T and N(X)=S, are considered. We present lower and upper bounds for the perturbation of AT,S(2). Convergence of subproper splittings for computing the special solution AT,S(2)b of restricted rectangular linear system Ax=b, x∈T, are studied. For the solution AT,S(2)b we develop a characterization. Therefore, we give a unified treatment of the related problems considered in literature by Ben-Israel, Berman, Hanke, Neumann, Plemmons, etc.